Existence of simple non-cyclic abelian varieties over arbitrary finite fields and of a given dimension $g>1$
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915379623755776 |
|---|---|
| author | Maidana, Alejandro J. Giangreco |
| author_facet | Maidana, Alejandro J. Giangreco |
| contents | Vl{\u a}du{\c t} characterized in 1999 the set of finite fields $k$ such that all elliptic curves defined over $k$ have a cyclic group of rational points. Under the conjecture of infinitely many Mersenne primes, this set is infinite. In these notes we prove that there is no a finite field $k$ such that all the simple abelian varieties defined over $k$ of dimension $g>1$ have a cyclic group of rational points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06916 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence of simple non-cyclic abelian varieties over arbitrary finite fields and of a given dimension $g>1$ Maidana, Alejandro J. Giangreco Algebraic Geometry Number Theory 11G10, 14G15, 14K15 Vl{\u a}du{\c t} characterized in 1999 the set of finite fields $k$ such that all elliptic curves defined over $k$ have a cyclic group of rational points. Under the conjecture of infinitely many Mersenne primes, this set is infinite. In these notes we prove that there is no a finite field $k$ such that all the simple abelian varieties defined over $k$ of dimension $g>1$ have a cyclic group of rational points. |
| title | Existence of simple non-cyclic abelian varieties over arbitrary finite fields and of a given dimension $g>1$ |
| topic | Algebraic Geometry Number Theory 11G10, 14G15, 14K15 |
| url | https://arxiv.org/abs/2507.06916 |